MULTIPLE LINEAR REGRESSION


A special class of statistical techniques, called multivariate methods , is used for studying the relationships among several interrelated variables . The goals of such multivariate analyses may be quite different from that of a univariate analysis, but they share many common features. Here we will take a look at some of the most popular ones.

You can use multiple linear regression analysis to study the relationship between a single dependent variable and several independent variables of the form.

Y = Constant + B 1 X 1 + B 2 X 2 + B 3 X 3 ... B n X n

The model looks like the regression model we already have seen. The difference is that you now have several variables on the independent variable side of the model. The independent variables are indicated by X 1 , X 2 , X 3 , ..., X n and the coefficients by B 1 , B 2 , B 3 , ..., B n . As before, the method of least squares can be used to estimate all of the coefficients.

Perhaps the most important issue with multiple linear regression is that because the variables are measured in different units, you cannot just compare the magnitudes of the coefficients to one another. Because of this characteristic, the experimenter must standardize the variables in some fashion. That standardization takes place with a statistic called BETA and contains the regression coefficients when all variables are standardized to a mean of zero and a standard deviation of one. Of course, just like before we still use the significance test for the test of the null hypothesis that the value of a coefficient is zero in the population. You can see that the null hypothesis can be rejected for all of the variables.

When you build a model with several interrelated independent variables, it is not easy to determine how much each variable contributes to the model. You cannot just look at the coefficients and say this is an important variable for predicting the dependent variable and this one is not. The contributions of the variables are "shared." The goodness-of-fit statistics we considered for a regression model with one independent variable can easily be extended to a model with multiple independent variables.




Six Sigma and Beyond. Statistics and Probability
Six Sigma and Beyond: Statistics and Probability, Volume III
ISBN: 1574443127
EAN: 2147483647
Year: 2003
Pages: 252

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